The present invention can blindly de-mix a single pixel of underlying unknown sources cases whether the sources are generated by associated heat of warm blood supply needed for a rapid growth of tumor or artificially induced by molecular tagging of fluorescence proteins; and whether the spectrum is infrared radiation, visible fluorescence or invisible Tera-Hertz radio frequency, which are all by definition unknown sources to be identically treated using statistical-mechanics paradigm.
Tumor identification based on algorithms (or procedures) using multiple-pixel statistics assuming that a tumor is larger than a pixel is known in the art. More particularly, a statistical, multiple pixel, blind source separation algorithm (procedure), termed ICA (Independent Component Analysis), is known in the art and is based on the factorization of joint probability density. However, these algorithms require that a tumor has reached sufficient size, that is, larger than a pixel, so that its neighborhood can contribute to the determination of the identical mixing matrix [A] shared by all pixels without more unknowns as in the opposite limit of a small tumor having the space-variant [A] for different pixels. In other words, an image of the tumor spreads across at least several neighborhood pixels having similar mixing matrix before the tumor can be identified.
That is, other statistical Independent Component Analyses (ICA) methodologies suffer pixel-averaging blurring effects since the average over neighborhood pixels must implicitly assume an identical breast-medium heat transfer matrix MTF [A] for the space-invariant imaging. This would be true only for a large tumor requiring no earlier target detection.
It would be more desirable to detect a tumor as early as possible in the life cycle of the tumor, before the tumor has reached sufficient size to spread across more than one pixel.
Standard Blind Source Separation (BSS) is known in the art, and is referred to as “Bell-Sejnowski, Amari, and Oja (BSAO)”—four groups of researchers. “BSAO” has addressed the linear version of BSS. “BSAO” assumed the identical mixing matrix for all pixels using the Artificial Neural Network (ANN) as all pixel data post-processing collectively in order to factorize the joint-probability density function of all pixels known mathematically as the Independent Component Analysis (ICA). The BSAO ICA unsupervised learning methodology searches for the natural gradient of Artificial Neural Networks (ANN) post-processing weight matrix [W] by means of a typical contrast function: Maximum Entropy (MaxEnt) of integral version of the neurons' outputs:
            ∂              [        W        ]                    ∂      t        =            〈                                                                  ∂                                  H                  ⁡                                      (                                                                  y                        →                                            ⁡                                              (                                                                              [                            W                            ]                                                    ⁢                                                      x                            →                                                                          )                                                              )                                                                              ∂                                  [                  W                  ]                                                      ⁡                          [              W              ]                                T                ⁡                  [          W          ]                    〉              pixels      ⁢              x        _            where BSAO's H is the Shannon entropy S of which the natural gradient Riemannian metric of the data distance followed from the Euclidean distance of the neuron output ({right arrow over (y)},{right arrow over (y)})=({right arrow over (x)}[W]T[W]{right arrow over (x)}), as shown in FIG. 1.
FIG. 1 is an illustration of the “BSAO”, MaxEnt Neural Network 100 of the related art which implements natural gradient based unsupervised learning methodology searching for the post-processing weight matrix [W] (or [W]) by means of a typical contrast function: Maximum Entropy (MaxEnt) of integral version of the neuron's output.
The MaxEnt Neural Network 100 used the pixel ensemble average for the stochastic gradient assuming the same mixing matrix [A] (or [A]) for all the pixels and was consequently non-real-time batch mode algorithm. In multi-spectral imaging applications (remote sensing, breast cancer detection, fiber-optic data gathering in tissue) the ensemble average property will cause a loss of details that in some cases (breast cancer detection, detection of small objects in the remote sensing) could be unacceptable.
In addition, a single-pixel, remote-sensing ad hoc method, a feedback, linear, Lagrange Constraint Neural Network, by H. Szu is known in the art. This method is based on a gradient descent (or slope) method and is applicable to the far-field radiation linear problems only. However, real world applications are mostly nonlinear or pseudo-linear.
FIG. 2 shows a single color (short, mid or long IR) breast imaging system 200, which includes single cameras 202 for each of the spectrum colors each of which has different optical axis, and a computer 204 executing a single color infra-red (IR) breast image processing and classification procedure known in the art. Infrared (IR) breast imagining of the related art is based on a single integrated spectral band on either the long (8-12 μm), the mid (3-4 μm), or short IR (1-3 μ), shown in FIG. 2, but not on all simultaneously capable for fusion and self-classification.
FIG. 3 is optical layout of a single-mode fiber-optic endoscope 300 of the related art. In situ fiber-optical data gathering or imaging devices of the related art are based on single mode of optical sensing, an example of which is shown in FIG. 3. In the single-mode fiber-optic endoscope 300, light reflected from tissue 302 is directed by objective lens 304 into the single-mode fiber relay 306 to ocular lens 308 and to detector array 301 which detects light of only a single wavelength.
FIG. 4 is a single ear based selective amplification hearing system 400, in which signal+noise is transmitted by detector 402 to a PDA-like device 404 which is transmitted to an earpiece 406. By using a single sensor (one ear) 402 system it becomes more difficult to cancel the noise or interference. Selective amplification hearing aids 400 of the related art are based on a single inner ear cochlear mechanism, as shown in FIG. 4.
Thermal breast scanning has been employed for a number of years, especially in Europe and Asia, but its use has been limited to a single integrated infra-red band, using a single camera and compared in a chill room about ten minutes the differential cooling rate of malign and benign tumor. Unfortunately, this procedure has generated too much variability to be reliable and reproducible.
In addition, supervised algorithms are known in the art. In supervised algorithms, a standard library is needed but each person is unique in tumor development and personal response physiology that a supervised library approach will create a biased estimation.
Further, trained, supervised neural networks used for medical applications are known in the art. Supervised networks have the limitation of requiring another method of accurately determining the value of the parameter under different conditions. Further, the accuracy of supervised networks is dependent upon the amount of such available “training”.
An unsupervised learning process separating unknown source signals with both mixture characteristics and original sources unknown, but using independent component analysis (ICA), which assumes spatial invariance, is known in the art. That is, the assumption is made that mixing matrices of the sources represented in nearby pixels are the same. Spatial invariance assumptions are appropriate for images with high pixel on target values (that is, an image of a large tumor), but lead to significant error when applied to images with small pixel on target values (that is, an image of a small tumor or pre-tumor). Thus, harnessing the ICA algorithm to detect small growths or other such aberrations that can not characterize the early stages of a pathological disorder.
In addition, a Fast Simulated Annealing algorithm by H. Szu is known in the art (Szu and Hartley, “Fast Simulated Annealing”, Physical Letters A, volume 122, number 3, pp. 157-162, 1987, the contents of which are incorporated herein by reference).